确定性均匀递归树的拓扑和Laplacian谱
Topologies and Laplacian spectra of a deterministic uniform recursive tree
摘要：
统一递归树（URT）是一种重要的模型，在许多领域都有成功的应用。本文研究了确定性均匀递归树的Laplacian矩阵的拓扑特征和谱性质，它是URT的确定性版本。首先，从复杂网络的角度出发，确定了确定树的主要结构特征。结果表明，该网络具有指数度分布、较小的平均路径长度、幂律分布的节点介数和正的度-度相关性.然后，我们确定所考虑的图的完全拉普拉斯谱（特征值）和它们相应的特征向量。有趣的是，所有的拉普拉斯特征值都是不同的。
英文摘要：
The uniform recursive tree (URT) is one of the most important models and has been successfully applied to many fields. Here we study exactly the topological characteristics and spectral properties of the Laplacian matrix of a deterministic uniform recursive tree, which is a deterministic version of URT. Firstly, from the perspective of complex networks, we determine the main structural characteristics of the deterministic tree. The obtained vigorous results show that the network has an exponential degree distribution, small average path length, power-law distribution of node betweenness, and positive degree-degree correlations. Then we determine the complete Laplacian spectra (eigenvalues) and their corresponding eigenvectors of the considered graph. Interestingly, all the Laplacian eigenvalues are distinct.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
